Question

Arrhenius studied the effect of temperature on the rate of a reaction and postulated that rate constant varies with temperature exponentially as $k=A{e}^{-\frac{E_a}{RT}}$ This method is generally used for finding the activation energy of a reaction. Keeping temperature constant, the effect of catalyst on the activation energy has also been studied.
If x is the fraction of molecules having energy greater than $E_a$ it will be given by:

• A. $x=\frac{E_a}{RT}$
• B. $lnx=-\frac{E_a}{RT}$
• C. $x=e^{E_a\times RT}$
• D. Any of these

Answer 1

The correct option is B $lnx=-\frac{E_a}{RT}$

In the Arrhenius equation the factor $e^{\frac{-Ea}{RT}}$ corresponds to the fraction of molecules that have kinetic energy greater than Ea.
$x=e^{-\frac{E_a}{RT}}$

Taking natural logarithm of both sides of the equation
$lnx=-\frac{E_a}{RT}$